When a Pokémon Transforms into Arceus, it becomes Arceus's Normal form. If it is holding a Plate, it will Transform first into Arceus's current form and will then change type and appearance to the type corresponding to that Plate.

Generation V

A Pokémon with Multitype cannot be affected by type changing moves, such as Soak. A Pokémon with Multitype is unaffected by Entrainment and Simple Beam. Multitype cannot turn into Mummy.

In the anime

The non-white parts of Arceus's body glow white. It then changes its color freely to match the type of the type it is forming into. A yellow ripple then forms throughout its body when it wants to change back to normal and its body goes back to its original colors.

Trivia

In the games, Arceus must be holding a Plate in order to make use of Multitype. However, in the anime and Pokémon Adventures, it has its own unique set of Plates which allow it to activate its Ability at will.